V.G. Luppov

University of Michigan

June 9, 2003

Storage of Polarized Atomic Hydrogen

OUTLINE

1. Introduction2. Electron-spin-polarized atomic hydrogen storage

2.1 Principle2.2 Michigan apparatus

3. Target thickness4. Target electron spin polarization5. Unpolarized Gas Backgrounds:

5.1 Metastable H 2s state5.2 Helium Background5.3 Accelerator Residual Gas Background5.4 H2 Background Due to Recombination Processes

6. Possible layout for Møller Polarimetry7. Conclusions

51 mK

17 mK

4⟩ = − ↓⇑⟩ + ε ↑⇓⟩

2⟩ = ↑⇓⟩ + ε ↓⇑⟩

1⟩ = ↑⇑⟩

3⟩ = ↓⇓⟩

10.8K at 8T

68 mK

Schematic Hyperfine Energy Level Diagram of Hydrogen Atom in Magnetic Field

↑ - electron spin, ⇑ - proton spin

In order to stabilize atomic hydrogen:

- atoms must be made (by dissociating H2 );- the electron spins must be polarized;- the spin polarization must be maintained;- the atomic hydrogen must be confined to a cell; - the hydrogen surface recombination must be suppressed.

For atomic hydrogen at B = 8 T and T = 300 mK, ratio electron spins-down to spins-up is exp(2µBB/kT)= 3.6⋅1015

Electron spin “down”

(High Field Seekers-HFS)

Electron spin “up”

(Low Field Seekers-LFS)E(K)

B(T)

Potential Energy of Low Field Seekers ( |1> and |2> ) and High Field Seekers ( |3> and |4> ) Along the Solenoid Axis

Storage Cell Displayed Relative to the Solenoid Field Profile

Hout ( 300 mK)

Mixing Chamber (300 mK) Coated with Superfluid He4 Film

Hin ( 30K)

Schematic Diagram of the Michigan Target

__________20 cm

8 Tesla Solenoid

Still (~ 900 mK)

Dissociator

Mixing Chamber (300 mK)

H2 Inlet

H

The probability that the electron spin-up atoms enter the Stabilization Cell

p = e-µB/kT

1.00E-101.00E-091.00E-081.00E-071.00E-061.00E-051.00E-041.00E-031.00E-021.00E-011.00E+00

0 1 2 3 4 5 6 7 8 9 10

Magnetic Field (T)

Prob

abilit

y

where µ - Bohr magneton (9.27⋅10 -24 J/T),

B - magnetic field,

K - Boltzmann constant (1.38⋅10 -23 J/K),

T - temperature (T ≡ 300 mK).

Confinement Time

dn/dt = – n/τes, where τes = τesoeµB/kT

For storage cell with diameter of 4 cm, effective lentgh of 19 cm,

and for n = 1016 atoms/cm3, T = 300 mk and B=0

τeso ~ 4 sec

For 8 Tesla magnetic field τconf= 2x108 sec: an ideal trap

Confinement Time

1.00E+00

1.00E+02

1.00E+04

1.00E+06

1.00E+08

1.00E+10

0 2 4 6 8 10

Magnetic Field (T)

Conf

inem

ent T

ime

(sec

)

Stored Atomic Hydrogen Density vs Magnetic Field for Different H Feed Rates (T=0.3 K)

1.00E+12

1.00E+13

1.00E+14

1.00E+15

1.00E+16

1.00E+17

0 2 4 6 8 10

Solenoid Magnetic Field (T)

Den

sity

(a

tom

s/cm

3 ) 1x10^16atoms/sec5x10^15atoms/sec1x10^15atoms/sec

Stored Atomic Hydrogen Thickness vs Magnetic Field for Different H Feed Rates (T=0.3 K)

1.00E+13

1.00E+14

1.00E+15

1.00E+16

1.00E+17

1.00E+18

0 2 4 6 8 10

Solenoid Magnetic Field (T)

Thic

knes

s (a

tom

s/cm

2 )

1x10^16atoms/sec5x10^15atoms/sec1x10^15atoms/sec

Stored Atomic Hydrogen Density vs Temperature (B =8 T)

1.00E+13

1.00E+14

1.00E+15

1.00E+16

1.00E+17

0 0.1 0.2 0.3 0.4 0.5

Temperature (K)

Den

sity

(ato

ms/

cm3 ) 1x10^16atoms/sec

5x10^15atoms/sec

1x10^15atoms/sec

M.Mertig et al,Rev.Sc.In. 62(1), 1991

Atomic Hydrogen Density MonitoringEither a capacitive pressure gauge(Matthey, A.P.M., Walraven, J.T.M., and Silvera, I.F., Phys. Rev.Lett. 46, 668 (1981)),

or a bolometer monitor(Mertig, M., Luppov, V.G., Roser, T., and Vuaridel B., Rev.Sci. Instrum., 62(1), 251 (1991))

could be used for continuous atomic hydrogen density measurements.

Target Electron-Spin- Polarization

↑ - electron spin, ⇑ - proton spin

For the mixed state |4> the fraction of electron–spin–up atoms is tan2 θ,

where θ = 1/2⋅arctan(a/[h(γe + γp )B],a = 9.42⋅10-25 [J] - hyperfine coupling constant,γe = ge·µB/ħ = 2.80⋅1010 [T-1s-1] = electron gyromagnetic ratio,γp = gn·µn/ħ = 4.26⋅107 [T-1s-1] = proton gyromagnetic ratio.

51 mK

17 mK

4⟩ = − ↓⇑⟩ + ε ↑⇓⟩

1⟩ = ↑⇑⟩

3⟩ = ↓⇓⟩

10.8K at 8T

Electron spin “down”

(High Field Seekers-HFS)

Electron spin “up”

(Low Field Seekers-LFS)E(K)

B(T)

2⟩ = ↑⇓⟩ + ε ↓⇑⟩

68 mK

Electron Spin-up Fraction vs. Magnetic Field

1.00E-06

1.00E-05

1.00E-04

1.00E-03

0 2 4 6 8 10

Magnetic Field (T)

Frac

tion

of E

lect

ron

Spin

-up

Density Distribution in 8 T Solenoid's Magnetic Field

n(z) = n(B0)exp[-µ(B0-Bz(z))/kT]

1.00E-081.00E-071.00E-061.00E-051.00E-041.00E-031.00E-021.00E-011.00E+00

02468

Magnetic Field (T)

Den

sity

(arb

.uni

ts)

Polarization “Self-Cleaning” Mechanism

Escape time for gradB = 0τ esc ~ 4 sec

As soon as low field seekers enter grad B they will be pushed out.

Hout ( 300 mK)

Mixing Chamber

Hin ( 30K)

Depolarization Processes (3> → 2> )dn2/dt =ξK333n3

3 + G32n32– n2/τes0,

where K333 - three-body recombination rate constant (K333≈9·10-39 cm6/sec),

ξ = 0.91 – a fraction of {3> + 3> + 3> → H2 + 2>}

(1- ξ) → {3> + 3> + 3> → H2 + 3>}

G32 – electronic relaxation rate constant (G32 = 1.1·10-15exp(-1.35B/T) cm3/sec)

τes0 = 4 sec

For B = 8 T, T=300 mK and (n3 + n4) ↓ = 1016 atoms/cm3 :

n2↑ = 4·109 atoms/cm3

Metastable 2S StatePermitted Transitions Between Different H Energy Levels and Life Times

2S and 2P States in Magnetic Field

τ = 1.56·10-8 sec

τ = 0.54·10-8 sec

τ = 16·10-8 sec

τ = 0.16·10-8 sec

∞τ =

WeakField

Strong Field

B=0

2S1/2

2P1/2

2P3/2

LFS

HFS

Metastable 2S1/2 states with different electron spins from the dissociator will be separated by the magnetic field gradient when they enter the storage cell.

Gas Backgrounds● Helium Background

Typical He pressure of ~ 10-6 Torr corresponds to~ 2.4⋅1010 atoms/cm3 or ~ 4.8⋅1010 electrons/cm3 at T = 300 K or ~ 7.6⋅1011 atoms/cm3 or ~ 1.5⋅1012 electrons/cm3 at T = 300 mK.

It gives about 0.02% unpolarized electrons density background for stored densityof 1016 electrons/cm3.

● Accelerator Residual Gas Background (by EAC)

Typical Jlab residual gas (H2O and N2) pressure of ~ 10-5 Torr corresponds to~ 2.4⋅1011 moleculers/cm3 or ~ 3⋅1012 electrons/cm3 at T = 300 K.It gives about 0.03% unpolarized electrons density background for stored density of 1016 electrons/cm3.

● H2 Background Due to Recombination Processes

For stored H density of 1016 atoms/cm3 molecular hydrogen density in the cell is about 2⋅1010 H2/cm3.

Radiation Heat Load (Qrad) to the Storage Cell

A surface emits thermal radiation according to the Stefan-Boltzmann equation:W = σ·e ·A ·T4 ,

where σ = 5.67·10-12 Watt · cm-2 ·T-4, e = total emissivity (~0.1 for copper), A = area, T = temperature.

Rather complex: T=300 K or 80 K for different parts.For the proposed geometry

Qrad ~ 1mW << 20 mW = dilution fridge cooling power at 300 mK.

Jefferson Lab Hall A Møller Polarimeter Layout

Possible H Target Layout

Conclusions

● The considerations above show that 100% longitudinally electron-spin-polarized

atomic hydrogen can be stored and used as a pure gas target.

● A thickness of at least 1·1017 H/cm2 can be reached with a target diameter of 4 cm

and a length of 19 cm along the beam.

● The polarized atomic hydrogen storage technique is well established, broadly studied,

and very reliable.